The initial Q-value defined in Eq. REF  combines the factors of the selection and sorting of candidate cities in LK ([1]} [1]}) and LKH ([3]} [3]}), which are the distance and the \(\alpha \) -value, respectively. The purpose of \(w(\pi )\)  is two-folds. First, it can prevent the initial Q-value from being much smaller than the rewards. Second, it can adaptively adjust the initial Q-value for different instances. In particular, Zheng et al. ([5]}) empirically demonstrate that the LKH algorithm can be improved only by replacing the \(\alpha \) -value in LKH with the initial Q-value.
